Force & Deflection While Dumping Material Into Bin

[PhilBW]

I am designing a 5' diameter bin which will be filled from a larger bin above. We will dump 75 cu. ft., or approx. 3000 lb., of material into the lower bin in around 5 seconds. I know the normal calculations for sudden impact, but how do you calculate the force and deflection for a falling mass when it is a flowing material instead of all one chunck of mass?

Phil

 

[vc66]

Why not just calculate it for 3000 lbs?

That's your worst case scenario, isn't it?

V

 

[PhilBW]

The static load is 3000 lb., but the dynamic load will be something greater because the product is accelerating as it falls. The velocity of the material will cause a momentary spike in the force on the bottom and structure of the bin that needs to be considered. Once all the product is in the bin and its velocity is 0, only the static force from the 3000 lb. applies.

If the material fell as a solid chunk, according to Roark the ratio of the stress as the product hit the bottom of the bin compared to the stress of the static load is 1 + sqrt(1 + 2h/d), where h = height of fall and d is displacement during static loading. Since the material doesn't fall as a solid chunk, this equation can't be used.

Phil

 

[vc66]

I guess I still don't understand. If you have 3000 lbs of stuff, and it's sitting there in a bin--it's 3000lbs of stuff. I don't understand how a solid chunk of 3000 lbs is going to give you less stress or deflection than a gradual increase to 3000 lbs. So if you calculate a 3000 lb block falling into a bin, won't that be the maximum amount of deflection, i.e. you're assuming that all of the 75 cu ft of material falls in the first increment of time?

I'm sorry if I'm missing something.

V

 

[PhilBW]

If the product is just sitting in the bin, the 3000 lb. is all that needs to be considered. But it is not sitting there, it is falling from a distance of 7 feet.

Something falling onto a surface imparts a much higher force on the surface than if it is just sitting on the surface. The farther it drops, the higher velocity it has and the higher force it causes.

Phil

 

[IRstuff]

You guys are dancing around the same subject. Given the distributed nature of the material and the longish time to dump the load, the impact load will probably never exceed the static load.

A compromise approach would be to treat the dump as a series of small chunks, each impacting immediately after the other, spread out over 5 seconds.

TTFN

FAQ731-376

 

[PhilBW]

IRstuff:

I knew that the longer it takes for all of the material to fall in the bin, the less impact the fall would have. However, I didn't know if 5 seconds was long enough.

I might try your suggestion of treating it as a bunch of small chunks and see how chunk size affects the force.

Phil

 

[IRstuff]

A typical car crash into a solid barrier is over in about 0.1 seconds. At 60 mph, this results in 27 g deceleration. The same speed, but a 5-s impact results in a 0.5-g deceleration.

So, even with small, solid chunks, there'll be some degree of overdesign.

TTFN

FAQ731-376

 

[PeterCharles]

To see what's happening I might be tempted to get my wife's kitchen scales and a 2lb bag of sugar. Pour the sugar onto the scales from a height of 3 ft over a few seconds and see what the scale reads.

I've just had another thought while writing this, consider it as a fluid mass flow rate impacting a surface.
The force is the mass flow rate x impact velocity.

So estimate the time to discharge the 3000 lb into the lower bin to give the mass flow rate. The impact velocity is
v^2 = 2 x g x h . There's an estimate of the impact force.

 

[rb1957]

i think that's a good analogy (continuous solid particles = fluid) ... but i would consider Mdot*V and the force due to the momentum of the fliud, and add the static weight on top of this.

 

[zekeman]

It's the time rate of change of momentum plus the gravitational force of the accumulated material that is resting in the bin. The momentum force is
W/gt*V
and V is the free fall velocity on impact.
W=weight
g = grav constant
t = time of evacuation of mass
F=3000/(32.2*5)*sqrt(2*32.2*7)=395
So at the end of the flow the total force would be
3395lb

 

[vims]

Have you thought about that you can get pockets in the upper bin. When the pocket collapses you can get "chunks" falling into the lower bin.

 

[bklauba]

Whether the material falls in chunks or something closer to a liquid is highly material dependent. Dry concrete mix, coal, and soy meal (with high moisture content) certainly can, others, sand, most grains, for instance, flow and act almost like liquid.

If you knew what the recoil time of the lower hopper was, you could break up the Roark into a series of events:

If you take your Roark eq factor, which is somewhat constant (although the height of fall will decrease as the bin fills), and have = x, then the force of a 3000 lbs. chuck falling would be 3000x. If you then broke this up into a series of events, each the length of the recoil time, with the total time of the series of events equally 5 seconds, you have an analysis that comes closer to describing reality.

The recoil time, however (a factor associated with the damping of the bin) will change as the bin fills. We see this all the time with the application of rotary electric vibrators. If operated on a full bin, such a vibrator will draw 70-80% of its FLA, but if the bin is empty, then the amp draw will double to triple, sometimes worse. (Without good O/L protection, the vibrator burns up.)


Also, the effective impact area of the material on the bin will expand as the material accumulates. You can estimate how much if you have the "angle of repose" data of the material, which is the angle the material mound will form as it accumulates. That is who many of the participants rightly believe this is not a big deal; there would be many more broken hoppers if their observations did not apply.

Thus, the hopper is likely subjected to something like impacting in the early part of the 5 second pour.

No sub for testing thou, to see what model appears to describe the real world.

BK

 

[PhilBW]

Thanks to everyone who took the time to respond.

The responses regarding impact force and momentum are exactly what I was looking for.

Phil